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| 书名： | Methods of Qualitative Theory in Nonlinear Dynamics Part Ii) | |
|---|---|---|
| 作者： | Shilnikov, Leonid P.; Shilnikov, Andrey L.; Turaev, Dmitry V. | |
| 出版时间： | 2001-09-27 | |
| ISBN： | 9789810240721(P-ISBN) ，9789812798558(O-ISBN) | |
| 摘要： | ||
| 摘要： | ||
书目详情：
ContentsIntroduction to Part IIChapter 7. STRUCTURALLY STABLE SYSTEMS7.1. Rough systems on a plane. Andronov-Pontryagin theorem7.2. The set of center motions7.3. General classification of center motions7.4. Remarks on roughness of high-order dynamical systems7.5. Morse-Smale systems7.6. Some properties of Morse-Smale systemsChapter 8. BIFURCATIONS OF DYNAMICAL SYSTEMS8.1. Systems of first degree of non-roughness8.2. Remarks on bifurcations of multi-dimensional systems8.3. Structurally unstable homoclinic and heteroclinic orbits. Moduli of topological equivalence8.4. Bifurcations in finite-parameter families of systems. Andronovs setupChapter 9. THE BEHAVIOR OF DYNAMICAL SYSTEMS ON STABILITY BOUNDARIES OF EQUILIBRIUM STATES9.1. The reduction theorems. The Lyapunov functions9.2. The first critical case9.3. The second critical caseChapter 10. THE BEHAVIOR OF DYNAMICAL SYSTEMS ON STABILITY BOUNDARIES OF PERIODIC TRAJECTORIES10.1. The reduction of the Poincare map. Lyapunov functions10.2. The first critical case10.3. The second critical case10.4. The third critical case. Weak resonances10.5. Strong resonances10.6. Passage through strong resonance on stability boundary10.7. Additional remarks on resonancesChapter 11. LOCAL BIFURCATIONS ON THE ROUTE OVER STABILITY BOUNDARIES11.1. Bifurcation surface and transverse families11.2. Bifurcation of an equilibrium state with one zero exponent11.3. Bifurcation of periodic orbits with multiplier +111.4. Bifurcation of periodic orbits with multiplier -111.5. Andronov-Hopf bifurcation11.6. Birth of invariant torus11.7. Bifurcations of resonant periodic orbits accompanying the birth of invariant torusChapter 12. GLOBAL BIFURCATIONS AT THE DISAPPEARANCE OF SADDLE-NODE EQUILIBRIUM STATES AND PERIODIC ORBITS12.1. Bifurcations of a homoclinic loop to a saddle-node equilibrium state12.2. Creation of an invariant torus12.3. The formation of a Klein bottle12.4. The blue sky catastrophe12.5. On embedding into the flowChapter 13. BIFURCATIONS OF HOMOCLINIC LOOPS OF SADDLE EQUILIBRIUM STATES13.1. Stability of a separatrix loop on the plane13.2. Bifurcation of a limit cycle from a separatrix loop of a saddle with non-zero saddle value13.3. Bifurcations of a separatrix loop with zero saddle value13.4. Birth of periodic orbits from a homoclinic loop the case dim Wu = 1)13.5. Behavior of trajectories near a homoclinic loop in the case dim Wu > 113.6. Codimension-two bifurcations of homoclinic loops13.7. Bifurcations of the homoclinic-8 and heteroclinic cycles13.8. Estimates of the behavior of trajectories near a saddle equilibrium stateChapter 14. SAFE AND DANGEROUS BOUNDARIES14.1. Main stability boundaries of equilibrium states and periodic orbits14.2. Classification of codimension-one boundaries of stability regions14.3. Dynamically definite and indefinite boundaries of stability regionsAppendix C: Examples Problems & ExercisesBibliographyIndex - Parts I & II
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